spoj 2319 BIGSEQ - Sequence

You are given the sequence of all K-digit binary numbers: 0, 1,..., 2K-1. You need to fully partition the sequence into M chunks. Each chunk must be a consecutive subsequence of the original sequence. Let Si (1 ≤ i ≤ M) be the total number of 1's in all numbers in the ith chunk when written in binary, and let S be the maximum of all Si, i.e. the maximum number of 1's in any chunk. Your goal is to minimize S.

Input

In the first line of input, two numbers, K and M (1 ≤ K ≤ 100, 1 ≤ M ≤ 100, M ≤ 2^K), are given, separated by a single space character.

Output

In one line of the output, write the minimum S that can be obtained by some split. Write it without leading zeros. The result is not guaranteed to fit in a 64-bit integer.

Example

Input:

3 4

Output:

4

题解：

from 算法合集之《浅谈数位类统计问题》

code：

 #include<cstdio>
 #include<iostream>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 char ch;
 bool ok;
 void read(int &x){
     for (ok=,ch=getchar();!isdigit(ch);ch=getchar()) if (ch=='-') ok=;
     for (x=;isdigit(ch);x=x*+ch-'',ch=getchar());
     if (ok) x=-x;
 }
 const int maxn=;
 int k,n;
 const int MAXN=;
 const int maxnum=;
 struct bignum{
     int len,v[MAXN];
     bignum(){memset(v,,sizeof(v)),len=;}
     bignum operator=(const char* num){
         memset(v,,sizeof(v));
         len=((strlen(num)-)>>)+;
         int j=,k=;
         for (int i=strlen(num)-;i>=;i--){
             if (j==maxnum) j=,k++;
             v[k]+=(num[i]-'')*j;
             j*=;
         }
         return *this;
     }
     bignum operator=(const int num){
         char a[MAXN<<];
         sprintf(a,"%d",num);
         *this=a;
         return *this;
     }
     bignum (int num){*this=num;}
     bignum (const char* num){*this=num;}
     bignum operator+(const bignum &a){
         bignum c;
         c.len=max(len,a.len);
         for (int i=;i<c.len;i++){
             c.v[i]+=v[i]+a.v[i];
             if (c.v[i]>=maxnum) c.v[i+]+=(c.v[i]/maxnum),c.v[i]%=maxnum;
         }
         while (c.v[c.len]) c.len++;
         return c;
     }
     bignum operator-(const bignum b){
         bignum a,c;
         a=*this;
         c.len=len;
         for (int i=;i<len;i++){
             if (a.v[i]<b.v[i]) a.v[i+]--,a.v[i]+=maxnum;
             c.v[i]=a.v[i]-b.v[i];
         }
         while (c.len>&&!(c.v[c.len-])) c.len--;
         return c;
     }
     bignum operator*(const bignum &a){
         bignum c;
         c.len=len+a.len;
         for (int i=;i<len;i++)
             for (int j=;j<a.len;j++){
                 c.v[i+j]+=v[i]*a.v[j];
                 if (c.v[i+j]>=maxnum) c.v[i+j+]+=(c.v[i+j]/maxnum),c.v[i+j]%=maxnum;
             }
         while (c.len>&&!(c.v[c.len-])) c.len--;
         return c;
     }
     bignum operator*(const int &a){
         bignum c=a;
         return *this*c;
     }
     bignum operator/(const int &b){
         bignum c;
         int x=;
         for (int i=len-;i>=;i--){
             c.v[i]=(x*maxnum+v[i])/b;
             x=(x*maxnum+v[i])%b;
         }
         c.len=len;
         while (c.len>&&!(c.v[c.len-])) c.len--;
         return c;
     }
     bignum operator+=(const bignum &a){*this=*this+a;return *this;}
     bignum operator-=(const bignum &a){*this=*this-a;return *this;}
     bignum operator*=(const bignum &a){*this=*this*a;return *this;}
     bignum operator/=(const int &a){*this=*this/a;return *this;}
     bool operator < (const bignum &x)const{
         if (len!=x.len) return len<x.len;
         for (int i=len-;i>=;i--)
             if (v[i]!=x.v[i]) return v[i]<x.v[i];
         return false;
     }
     bool operator > (const bignum &x)const{return x<*this;}
     bool operator <=(const bignum &x)const{return !(x<*this);}
     bool operator >=(const bignum &x)const{return !(*this<x);}
     bool operator ==(const bignum &x)const{return !(x<*this||*this<x);}
     bool operator !=(const bignum &x)const{return x<*this||*this<x;}
 };
 void write(bignum x){
     printf("%d",x.v[x.len-]);
     for (int i=x.len-;i>=;i--) printf("%0*d",,x.v[i]);
     puts("");
 }
 void read(bignum &x){
     static char num[MAXN<<];
     scanf("%s",num);
     x=num;
 }
 bignum l,r,m,pw2[maxn],sum[maxn],tmp,res,t,xx;
 int a[maxn];
 void init(){
     pw2[]=;
     for (int i=;i<=;i++) pw2[i]=pw2[i-]*;
     sum[]=;
     for (int i=;i<=;i++) sum[i]=sum[i-]*+pw2[i-];
 }
 void calc(){
     tmp=,res=;
     for (int i=;i<=k;i++) if (a[i]) res+=tmp+sum[i-],tmp+=pw2[i-];
 }
 void find(bignum lim){
     bool flag=(lim>=sum[k]);
     int tmp=;
     for (int i=k;i>=;i--){
         xx=sum[i-]+pw2[i-]*tmp;
         if (lim>=xx) lim=lim-xx,tmp++,a[i]=;
         else a[i]=;
     }
     if (!flag){
         for (int i=;i<=k;i++){
             a[i]^=;
             if (!a[i]) break;
         }
     }
 }
 bool check(){
     for (int i=;i<=k;i++) if (!a[i]) return false;
     return true;
 }
 bool check(bignum lim){
     bignum t=;
     int cnt=n;
     memset(a,,sizeof(a));
     while (cnt--){
         find(t+lim),calc(),t=res;
         if (check()) return true;
     }
     return false;
 }
 int main(){
     init();
     read(k),read(n);
     l=,r=sum[k];
     while (l!=r){
         m=(l+r)/;
         if (check(m)) r=m; else l=m+;
     }
     write(l);
     return ;
 }